Question

question 1 of 10 which sequence of transformations will result in an image that maps onto itself? a. reflect over the y - axis, and then reflect over the x - axis. b. reflect over the y - axis, and then reflect again over the y - axis. c. rotate 180 degrees counterclockwise about the origin, and then reflect across the y - axis. d. rotate 180 degrees counterclockwise about the origin, and then reflect across the x - axis.

Explanation:

Step1: Analyze option A

Reflecting over y - axis changes $(x,y)$ to $(-x,y)$. Then reflecting over x - axis changes $(-x,y)$ to $(-x, - y)$. This is not the original point, so A is incorrect.

Step2: Analyze option B

Reflecting over the y - axis changes $(x,y)$ to $(-x,y)$. Reflecting again over the y - axis changes $(-x,y)$ back to $(x,y)$. This maps the image onto itself.

Step3: Analyze option C

Rotating 180 degrees counter - clockwise about the origin changes $(x,y)$ to $(-x,-y)$. Reflecting across the y - axis changes $(-x,-y)$ to $(x,-y)$. This is not the original point, so C is incorrect.

Step4: Analyze option D

Rotating 180 degrees counter - clockwise about the origin changes $(x,y)$ to $(-x,-y)$. Reflecting across the x - axis changes $(-x,-y)$ to $(-x,y)$. This is not the original point, so D is incorrect.

Answer:

B. Reflect over the y - axis, and then reflect again over the y - axis.